What is the Greatest Common Factor of 66748 and 66752?

Greatest common factor (GCF) of 66748 and 66752 is 4.

GCF(66748,66752) = 4

We will now calculate the prime factors of 66748 and 66752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66748 and 66752.

How to find the GCF of 66748 and 66752?

We will first find the prime factorization of 66748 and 66752. After we will calculate the factors of 66748 and 66752 and find the biggest common factor number .

Step-1: Prime Factorization of 66748

Prime factors of 66748 are 2, 11, 37, 41. Prime factorization of 66748 in exponential form is:

66748 = 2² × 11¹ × 37¹ × 41¹

Step-2: Prime Factorization of 66752

Prime factors of 66752 are 2, 7, 149. Prime factorization of 66752 in exponential form is:

66752 = 2⁶ × 7¹ × 149¹

Step-3: Factors of 66748

List of positive integer factors of 66748 that divides 66748 without a remainder.

1, 2, 4, 11, 22, 37, 41, 44, 74, 82, 148, 164, 407, 451, 814, 902, 1517, 1628, 1804, 3034, 6068, 16687, 33374

Step-4: Factors of 66752

List of positive integer factors of 66752 that divides 66748 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 149, 224, 298, 448, 596, 1043, 1192, 2086, 2384, 4172, 4768, 8344, 9536, 16688, 33376

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66748 and 66752. The biggest common factor number is the GCF number.
So the greatest common factor 66748 and 66752 is 4.

Also check out the Least Common Multiple of 66748 and 66752